# Deltoidal hexecontahedron

Deltoidal hexecontahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Sladit |

Coxeter diagram | m5o3m |

Elements | |

Faces | 60 kites |

Edges | 60+60 |

Vertices | 12+20+30 |

Vertex figure | 20 triangles, 30 squares, 12 pentagons |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Related polytopes | |

Army | Sladit |

Regiment | Sladit |

Dual | Small rhombicosidodecahedron |

Conjugate | Great deltoidal hexecontahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | Yes |

Nature | Tame |

The **deltoidal hexecontahedron**, also called the **strombic hexecontahedron** or **small lanceal ditriacontahedron**, is one of the 13 Catalan solids. It has 60 kites as faces, with 12 order-5, 20 order-3, and 30 order-4 vertices. It is the dual of the uniform small rhombicosidodecahedron.

It can also be obtained as the convex hull of a dodecahedron, an icosahedron, and an icosidodecahedron. If the dodecahedron has unit edge length, the icosahedron's edge length is and the icosidodecahedron's edge length is .

Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges. These kites have one angle measuring , the opposite angle measuring , and the other two angles measuring .

## Related polytopes[edit | edit source]

The deltoidal hexecontahedron is topologically equivalent to the rhombic hexecontahedron which has golden rhombi for faces instead of kites.

## External links[edit | edit source]

- Klitzing, Richard. "Sladit".

- Wikipedia Contributors. "Deltoidal hexecontahedron".
- McCooey, David. "Deltoidal Hexecontahedron"

- Hi.gher.Space Wiki Contributors. "Deltoidal hexecontahedron".